I think most people just wanted Amazon to take the administrative overhead away from them. Amazon saw that gap.

Sure thing. That's the reason for many services they created.

But they usually tend to build their own alternative that integrates better into their eco-system.

They do. They've done similar things with Redis and MariaDB, both of whom also offer commercial solutions. The SAs all insist that "no it's a partnership". I don't fault them they're parroting the marketing line. With the new Grafana stuff that seems more like a real partnership because you have to purchase the enterprise features and support from the marketplace. What they've done to Redis and partiularly Elastic is pretty shameful.

The Elasticsearch Service has problems: you can't join the cluster like you can with the normal version, permissions are janky at best, it's slow, and it's expensive. For those reasons the projects my team used it on opted to roll our own elasticsearch cluster which proved a better solution long term beyond the initial annoyances. I say that to say it's not a one to one product, which will probably be their defense.